6533b7ddfe1ef96bd12752af
RESEARCH PRODUCT
Frames for fusions of modal logics
Sławomir Kostsubject
Class (set theory)LogicComputer scienceExistential quantificationFrame (networking)Multimodal logicMultimodal logic0102 computer and information sciences01 natural sciencesAlgebraPhilosophyModal010201 computation theory & mathematicsComputer Science::Logic in Computer SciencePoint (geometry)fusion of modal logicsdescription
Let us consider multimodal logics and . We assume that is characterised by a class of connected frames, and there exists an -frame with a so-called -starting point. Similarly, the logic is characterised by a class of connected frames, and there exists an -frame with a -starting point. Using isomorphic copies of the frames and , we construct a connected frame which characterises the fusion . The frame thus obtained has some useful properties. Among others, is countable if both and are countable, and there is a special world of the frame such that any formula is valid in the frame if and only if it is valid at the point . We also describe a similar construction where we assume the existence of two classes consisting of rooted frames only. Using those classes and frames with so-called -roots, we construct a rooted frame adequate for the fusion of modal logics characterised by the classes under consideration. Both constructions can be used interchangeably. The selection of the construction depends on the classes characterising the logics under consideration
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-01-02 | Journal of Applied Non-Classical Logics |